A model-based approach to shot charts estimation in basketball

Shot charts in basketball analytics provide an indispensable tool for evaluating players' shooting performance by visually representing the distribution of field goal attempts across different court locations. However, conventional methods often overlook the bounded nature of the basketball court, leading to inaccurate representations, particularly along the boundaries and corners. In this paper, we propose a novel model-based approach to shot charts estimation and visualization that explicitly considers the physical boundaries of the basketball court. By employing Gaussian mixtures for bounded data, our methodology allows to obtain more accurate estimation of shot density distributions for both made and missed shots. Bayes' rule is then applied to derive estimates for the probability of successful shooting from any given locations, and to identify the regions with the highest expected scores. Additionally, calibration plots are introduced to compare the estimated scoring probabilities with the observed proportions of made shots across different offensive areas, complemented by the normalized calibration error to summarize the overall goodness-of-fit of the model-based estimates. To illustrate the efficacy of our proposal, we apply it to data from the 2022/2023 NBA regular season, showing its usefulness through detailed analyses of shot patterns and calibration performance for two prominent players.